Decimals to Thousandths and Decimal Operations
Decimals to thousandths complete the decimal place value system students will use throughout secondary school. 0.375 is 3 tenths, 7 hundredths, 5 thousandths — or 375 out of 1000 equal parts of a whole. Thousandths appear in athletic timing (10.004 seconds), precise measurements (1.250 kg), and unit pricing ($2.375 per litre). Adding and subtracting decimals requires only one rule beyond whole-number arithmetic: align the decimal points so that tenths add to tenths, hundredths to hundredths, thousandths to thousandths.
Thousandths as place value
The place value pattern continues rightward: tenths (1/10), hundredths (1/100), thousandths (1/1000). Each position is 1/10 the size of the position to its left. 0.375 = 3/10 + 7/100 + 5/1000. Written as a single fraction: 375/1000. Simplified: 375 and 1000 share GCF=125: 375/1000 = 3/8. This is why 0.375 = 3/8 — a surprising decimal-fraction connection.
Comparing and ordering decimals
Is 0.375 greater or less than 0.38? Compare digit by digit: tenths: 3=3. Hundredths: 7 vs. 8. 8>7, so 0.38 > 0.375. A common mistake: students think 0.375 is bigger because it has more digits. More digits do not mean more value: 0.375 has a smaller hundredths digit than 0.380.
Decimal addition and subtraction
3.47 + 2.183: align decimal points. 3.470 + 2.183 (add a zero to make alignment explicit). Ones: 3+2=5. Tenths: 4+1=5. Hundredths: 7+8=15, write 5 carry 1. Thousandths: 0+3=3. Result: 5.653. Lining up decimal points is the only new requirement: all other arithmetic is place-value addition and subtraction already known.